tbsv

Solves a system of linear equations whose coefficients are in a triangular band matrix.

Description

The tbsv routines solve a system of linear equations whose coefficients are in a triangular band matrix. The operation is defined as

op(A)*x = b

where:

  • op(A) is one of op(A) = A, or op(A) = AT, or op(A) = AH,

  • A is an n-by-n unit or non-unit, upper or lower triangular band matrix, with (k + 1) diagonals,

  • b and x are vectors of length n.

API

Syntax

void tbsv(queue &exec_queue,
  uplo upper_lower,
  transpose trans,
  diag unit_nonunit,
  std::int64_t n,
  std::int64_t k,
  buffer<T,1> &a,
  std::int64_t lda,
  buffer<T,1> &x,
  std::int64_t incx)

tbsv supports the following precisions and devices.

T

Devices Supported

float

Host, CPU, and GPU

double

Host, CPU, and GPU

std::complex<float>

Host, CPU, and GPU

std::complex<double>

Host, CPU, and GPU

Input Parameters

exec_queue

The queue where the routine should be executed.

upper_lower

Specifies whether A is upper or lower triangular. See Data Types for more details.

trans

Specifies op(A), the transposition operation applied to A. See Data Types for more details.

unit_nonunit

Specifies whether the matrix A is unit triangular or not. See Data Types for more details.

n

Number of rows and columns of A. Must be at least zero.

k

Number of sub/super-diagonals of the matrix A. Must be at least zero.

a

Buffer holding input matrix A. Must have size at least lda*n. See Matrix Storage for more details.

lda

Leading dimension of matrix A. Must be at least (k + 1), and positive.

x

Buffer holding input vector x. The buffer must be of size at least (1 + (n - 1)*abs(incx)). See Matrix Storage for more details.

incx

Stride of vector x.

Output Parameters

x

Buffer holding the solution vector x.